Stability analysis and the route to chaos for laser diodes withoptical feedback

The sequence of phenomena that lead from a narrow linewidth state to coherence collapse in semiconductor lasers for an increasing level of optical feedback has been identified. Undamping of the relaxation oscillations, which is shown to be accurately predicted by an analytical stability analysis, initializes the route to chaos, but the laser generally enters quasiperiodic and frequency-locked states before ending up in the chaotic state of coherence collapse. The analysis identifies the laser parameters which are relevant for reducing the feedback sensitivity     

Detailed analysis of coherence collapse in semiconductor lasers

Experimental and theoretical studies of coherence collapse in GaAs/AlGaAs laser diodes with weak optical feedback show two distinct routes to chaos. In each case we observe undamped relaxation oscillations, then external cavity mode beating, and finally coherence collapse. When there is frequency locking between the relaxation oscillations and external cavity modes, a period doubling sequence is followed, otherwise the route to chaos is via quasiperiodicity     

Mode selection and stability of a semiconductor laser with weakoptical feedback

The authors present measurements that show that a semiconductor laser with weak optical feedback oscillates in the external-cavity mode with the narrowest linewidth rather than the mode with minimum threshold gain. A frequency fluctuation model that explains this narrowest linewidth operation is proposed. This model also correctly predicts mode-hopping frequencies. It is shown that the frequency span of the external-cavity modes determines the critical feedback level that causes coherence collapse     

Modulation performance of a semiconductor laser coupled to anexternal high-Q resonator

The dynamic response of a semiconductor laser coupled to an external resonator is studied using the single-mode rate equations modified to account for the dispersive feedback. Both the frequency and the damping rate of relaxation oscillations are affected by the feedback. The frequency chirp that invariably accompanies amplitude modulation is significantly reduced. The feedback also reduces the phase noise and the linewidth. To investigate the usefulness of external-resonator lasers in high-speed optical communication systems, the rate equation have been solved numerically to obtain the emitted chirped pulse; the pulse is propagated through the fiber, detected, and filtered at the receiver. The simulated-eye diagrams show that such lasers can be operated at high bit rates with negligible dispersion penalty owing to their reduced frequency chip     

准直透镜失调对Littman-Metcalf光栅外腔激光器线宽的影响

以光栅外腔半导体激光器的理论知识为基础,对Littman-Metcalf型外腔半导体激光器的工作原理进行了说明,并详细地讨论了外腔半导体激光器的线宽压窄以及模式选择机制,采用严格的耦合理论和光线变换矩阵推导了系统结构参数对光场耦合效率影响的计算公式。同时,对影响Littman-Metcalf外腔激光器输出激光线宽的几个重要因素进行了分析,重点讨论了系统中准直透镜位置失调导致的线宽变化规律。计算结果表明:合理地控制Littman-Metcalf光栅外腔半导体激光器的外腔参数可以将中心波长为785 nm半导体激光器的本征线宽压窄四个数量级,该外腔系统中准直透镜位置失调会影响系统出射光场与经外腔反馈光场之间的耦合效率,进而影响光栅外腔半导体激光器的输出线宽。     

Spectral properties of a semiconductor laser coupled to a single mode fiber resonator

The effect of optical feedback from a single mode fiber resonator on the instantaneous frequency fluctuation spectrum and on the field fluctuation spectrum of an AlGaAs semiconductor laser is studied theoretically and experimentally. Single mode fiber resonators of different lengths and finesses are used for the experiments. The minimum linewidth conditions are given and it is shown that the linewidth reduction ratio increases with the fiber resonator selectivity. The limit for multistability operation depends on the resonator finesse. Theory and experiments are found to be in good agreement. Finally, the effect of resonator loaded semiconductor laser phase noise on BER performance in optical DPSK heterodyne systems is theoretically analyzed.     

The critical amount of optical feedback, for coherence collapse insemiconductor lasers

The coherence times and critical feedback rates are calculated for a coherence collapsed single-mode semiconductor laser with external optical feedback. It is shown that, in contrast to what is suggested by certain numerical simulations, coherence collapse need not disappear when the linewidth enhancement parameter vanishes     

Semiconductor laser stabilization by external optical feedback

A report is presented on a general theory describing the effect of external optical feedback on the steady-state noise characteristics of single-mode semiconductor lasers. The theory is valid for arbitrarily strong feedback and arbitrary optical feedback configuration and spectrum. A generalized Langevin rate equation is derived. The equation is, in general, infinite order in d/dt constituting an infinite-order correction to the low-frequency weak-feedback analysis. The general formalism includes relaxation oscillations and permits analysis of the effect of feedback on the laser linewidth, frequency noise, relative intensity noise, and the relaxation oscillation sidebands in the field spectrum. The theory is applied to two important feedback configurations: the laser coupled to a single mirror and the laser coupled to a high-Q cavity     

Theory of the phase noise and power spectrum of a single mode injection laser

Spontaneous emission alters the phase and amplitude of the laser field. The amplitude changes induce relaxation oscillations, which cause additional phase changes while restoring the field amplitude to the steady state value. It was previously shown that the additional phase changes greatly enhance the linewidth. We show here that the additional phase changes also give rise to line shape structure in the form of additional peaks separated from the main peak by multiples of the relaxation oscillation frequency. The calculated mean square phase change and power spectrum are in good agreement with published observations.     

Spectral signature of relaxation oscillations in semiconductorlasers

A novel and relatively simple expression is given for the optical spectrum of a single-mode semiconductor laser which, due to the presence of relaxation oscillations, consists of a strong central line with a broad weak sideband at each side. The coupling between phase and amplitude fluctuations is included in this derivation and is shown to result in an asymmetry between the relaxation oscillation sidebands. This asymmetry can be used to determine the linewidth enhancement factor. Using optical heterodyne detection, the spectrum of a Fabry-Perot-type AlGaAs laser has been measured as a function of output power. Information on the dynamics of the relaxation oscillations was thus obtained. The power dependence of the frequency and damping of the relaxation oscillations allowed the spontaneous lifetime and the dependence of the gain on both carrier density (differential gain) and intensity (gain saturation) to be separately determined     

Mid-range coherent optical frequency domain reflectometry with aDFB laser diode coupled to an external cavity

The optical frequency of an external double cavity coupled laser diode was controlled via the phase of the feedback light. Strong linewidth and mode hopping reductions were obtained, extending coherent reflectometry with semiconductor sources to the range of hundreds of meters     

Transient effects in external cavity semiconductor lasers

In several important applications of external cavity operated semiconductor lasers, including studies for FM optical communication and frequency stabilized lasers for coherent communication systems, the transient response of the laser is of crucial importance. In this letter, we present a first study of the transient optical response following a step current excitation applied to an AlGaAs laser operating in a dispersive external cavity. The study shows for the first time that, for optical feedback near the gain peak of the laser, a steady state is reached after only three roundtrips in the external cavity. However, for optical feedback far (∼100 Å) from the gain peak, 20 or more roundtrips are required before a steady state can be reached. It is also shown that under certain operation conditions the optical feedback can induce damped relaxation oscillations at each subsequent roundtrip in the external cavity.     

Controling the linewidth of a semiconductor laser withphotorefractive phase conjugate feedback

A novel technique for narrowing the linewidth of a single laser diode using photorefractive phase conjugate feedback is presented. The behavior of this system can be modeled by adapting the previously developed theory to include the phase constraints of the phase conjugate external cavity. The experiments show excellent agreement with the model. This technique produces a stable, narrow linewidth in a semiconductor laser. The comparison to the conventional case is discussed     

Characteristics of a grating-external-cavity semiconductor lasercontaining intracavity prism beam expanders

A grating tuned external cavity semiconductor laser incorporating a gradient-index rod lens and a pair of intracavity silicon prism beam expanders was constructed using a configuration aimed at simultaneously achieving the following objectives: the ability to operate at any external cavity longitudinal mode without tuning gaps caused by residual resonances of the laser diode cavity, stable feedback coupling between the diode and external cavities, narrow optical linewidth, and a high degree of external cavity longitudinal sidemode suppression     

Stable operation range for laser diodes with an integrated passivecavity in the presence of external optical feedback

It is shown that a laser diode with an integrated passive cavity yields higher tolerable levels of feedback from distant reflections than an equivalent long solitary laser diode. To ensure this high tolerance for external feedback, the internal feedback level in the integrated passive cavity must be of the order of about 10%. Then the laser diode remains stable up to external feedback levels in excess of 1% even if the internal reflection phase is not carefully adjusted. External reflections from a cleaved fiber end are then not sufficient to drive the laser into coherence collapse, if realistic coupling efficiencies between laser diode and fiber are taken into account. The low feedback sensitivity is explained by the combination of the long effective length of the laser and a high relaxation resonance frequency. Therefore, quantum-well laser diodes with a long length and a high relaxation resonance frequency are likewise expected to exhibit low feedback sensitivity     

外腔半导体激光器单频输出的长期稳定

一、引言 由于光纤通讯、光纤传感、检测二光谱分析、频标、光陀螺等领域的需要；单频半导体激光器的研究近年来受到广泛重视并得到迅速发展，由于采用了长外腔选模技术，已实现了线宽小于100 kHz的单频输出~[1-3]。而频率长期稳定工作则刚刚开始~[4]。通常认为，造成半导体激光器输出频率漂移及跳模的原因是管芯温度和注入电流的波动，因此稳频工作     

Propriétés spectrales d’un laser semiconducteur soumis à une rétroaction optique externe

The rate equations of a semiconductor laser with external optical feedback are solved numerically. The method is applied to the case of simple optical feedback and to that of a high finesse external resonator. The spectral linewidth reduction, the damping of the relaxation oscillations and the influence of the resonant frequencies of the external resonator are discussed and compared for these two configurations.     

Optical feedback effects on the spectral linewidth of semiconductorlaser sensors using self-mixing interference

The spectral characteristics of a semiconductor laser are significantly affected by optical feedback in the active cavity of the diode. In this paper, the influence of weak optical feedback on the linewidth is examined and a new relationship proposed. Feedback-induced changes in the power spectral density are also determined by a theoretical analytical model, in good agreements with experiments. These results are then discussed for sensing applications using self-mixing interference, as the maximum range of distance and displacement sensors can be limited by half the coherence length of the laser diode modified by the optical feedback